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Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGK Model
Authors:Yongguang Cheng  Luoding Zhu &  Chunze Zhang
Abstract:This paper aims to study the numerical features of a coupling scheme between the immersed boundary (IB) method and the lattice Boltzmann BGK (LBGK)model by four typical test problems: the relaxation of a circular membrane, the shearing flow induced by a moving fiber in the middle of a channel, the shearing flow neara non-slip rigid wall, and the circular Couette flow between two inversely rotatingcylinders. The accuracy and robustness of the IB-LBGK coupling scheme, the performances of different discrete Dirac delta functions, the effect of iteration on the coupling scheme, the importance of the external forcing term treatment, the sensitivity ofthe coupling scheme to flow and boundary parameters, the velocity slip near non-sliprigid wall, and the origination of numerical instabilities are investigated in detail viathe four test cases. It is found that the iteration in the coupling cycle can effectivelyimprove stability, the introduction of a second-order forcing term in LBGK model iscrucial, the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability, and the emergence of both temporal and spatialfluctuations of boundary parameters seems to be the indication of numerical instability. These elaborate results shed light on the nature of the coupling scheme and maybenefit those who wish to use or improve the method.
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